Finite Group Databasebeta

← #13175923

Subgroups — #13175923

Order 1728.

2452 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
3#11723925C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C32×#882C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723630C211yesmaximal, characteristic, complemented
8#11723599C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10#11723539C211yesmaximal, characteristic, complemented
11#11723531C211yesmaximal, characteristic, complemented
12#11723525C211yesmaximal, characteristic, complemented
13#11723518C211yesmaximal, characteristic, complemented
14#11723479C211yesmaximal, characteristic, complemented
15#11723473C211yesmaximal, characteristic, complemented
16#10596060—31nomaximal
17#10594262—34nomaximal
18C23×C32×D3C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×D12C2211yescharacteristic
29C2×C32×D12C2211yescharacteristic, complemented
30D3×#638—24no—
31C2×#6291C2211yescharacteristic
32C2×#6291C2211yescharacteristic, complemented
33C2×#6291C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic
36C2×#6289C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C3⋊D3×D12—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×D3×D12—34no—
59C32×#120—31no—
60#64162—31no—
61#64147—31no—
62#64147—31no—
63#64146—31no—
64#64146—31no—
65#64144—31no—
66#64095—31no—
67#64093—31no—
68#64093—31no—
69#64093—34no—
70#64093—64no—
71#64092—31no—
72#64092D311yescharacteristic, complemented
73C22⋊C4×C3⋊D3—31no—
74C3×#883—34no—
75C3×#882D314yescomplemented
76#63983—34no—
77#63977—34no—
78#63958—34no—
79#63922—34no—
80#63921—34no—
81#63916—34no—
82#63910—34no—
83#63905—34no—
84#63890—34no—
85#63884—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—41no—
92C22×C32×D3—41no—
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×D3×C3⋊D3—41no—
100C2×D3×C3⋊D3—41no—
101C2×D3×C3⋊D3D414yescomplemented
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104#6312—22no—
105#6312—41no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊(C3⋊D3))—22no—
109C4×C3⋊(C3⋊D3)—41no—
110C3×#638—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4×C3⋊D3—22no—
115C32×#67—41no—
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118C32×D12—41no—
119#6291—22no—
120#6291—22no—
121#6291—22no—
122#6291—41no—
123#6290—22no—
124#6289—41no—
125D3×C3⋊Dic3—22no—
126#5653—91no—
127#5589—94no—
128C24×C32—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—31no—
131C23×C3×D3C2×D314yescomplemented
132C22×D32—34no—
133C22×D32—34no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—34no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—64no—
147C2×#638—64no—
148C2×#638—64no—
149C2×#638C2×D311yescharacteristic
150C22×C3⋊Dic3—31no—
151D4×C3⋊D3—64no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4⋊(C3⋊D3)—34no—
154C2×C4⋊(C3⋊D3)—64no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
160C2×C3×#67—34no—
161C2×C3×#67C2×D314yescomplemented
162C2×C3×D12C2×D314yes—
163C2×C3×D12C2×D314yescomplemented
164C2×C3×C4×D3—34no—
165D3×#67—616no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#625—34no—
171C2×#624—34no—
172C2×D3×Dic3—34no—
173D3×D12—616no—
174C32×C22⋊C4—24no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4C2×D314yescomplemented
178C32×C22⋊C4C2×D311yescharacteristic, complemented
179#3757—31no—
180#3757—31no—
181#3757—31no—
182#3757—31no—
183#3757C2×D311yescharacteristic, complemented
184#3752—31no—
185#3752—31no—
186#3752—34no—
187#3752—31no—
188#3752—64no—
189#3752C2×D311yescharacteristic, complemented
190C4⋊(C3⋊Dic3)—31no—
191C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
192#3750—31no—
193#3750—34no—
194#3750—64no—
195#3750C2×D311yescharacteristic, complemented
196C3×#217—34no—
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4C2×D314yescomplemented
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×C4⋊Dic3—34no—
201C3×Dic3⋊C4—34no—
202Dic3⋊Dic3—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)C2×D412yes—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3C2×D412yes—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—44no—
231C2×C32×D3C2×D412yes—
232D3×C3⋊D3—44no—
233D3×C3⋊D3—44no—
234C33×C4—21no—
235C33×C4—21no—
236C3⋊(C3⋊Dic3)—21no—
237C3⋊(C3⋊Dic3)—21no—
238C3×C3⋊Dic3—21no—
239C3×C3⋊Dic3—21no—
240C3×C3⋊Dic3—21no—
241C32×Dic3—21no—
242C22×#67—94no—
243C2×D3×D4—94no—
244C2×D3×D4—91no—
245C22×D12—91no—
246C3×#123—91no—
247C3×#120—34no—
248#953—94no—
249#938—94no—
250#938—94no—
251#937—94no—
252#937—94no—
253#937—91no—
254#935—94no—
255#929—91no—
256#895—91no—
257#895—91no—
258#894—91no—
259#894—91no—
260#886—94no—
261#884—94no—
262#884—91no—
263#884—94no—
264#884—91no—
265#884—184no—
266#883—34no—
267#883—94no—
268#882—91no—
269#882—91no—
270#882C3⋊D311yescharacteristic, complemented
271D3×C22⋊C4—94no—
272D3×C22⋊C4—91no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32—31no—
277C23×C32—62no—
278C23×C32—121no—
279C23×C32—121no—
280C23×C32C22×D314yes—
281C23×C32C22×D311yescharacteristic
282C22×C3⋊D3—31no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—31no—
285C22×C3⋊D3—34no—
286C22×C3⋊D3—34no—
287C22×C3⋊D3—64no—
288C22×C3⋊D3—64no—
289C22×C3⋊D3—62no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—121no—
294C22×C3⋊D3C22×D311yescharacteristic
295C22×C3×D3—28no—
296C22×C3×D3—34no—
297C22×C3×D3—44no—
298C22×C3×D3—44no—
299C22×C3×D3C22×D314yes—
300C22×C3×D3C22×D314yes—
301C22×C3×D3C22×D314yes—
302C2×D32—316no—
303C2×D32—68no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—124no—
307C2×D32—124no—
308C32×D4—62no—
309C32×D4—121no—
310C32×D4—121no—
311C2×C32×C4—24no—
312C2×C32×C4—24no—
313C2×C32×C4—31no—
314C2×C32×C4C22×D314yes—
315C2×C32×C4C22×D314yes—
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318#638—22no—
319#638—62no—
320#638—62no—
321#638—62no—
322#638—62no—
323#638—62no—
324#638—68no—
325#638—128no—
326#638—121no—
327#638—121no—
328#638—124no—
329#638—128no—
330C2×C3⋊Dic3—31no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—34no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—64no—
336C2×C3⋊Dic3—62no—
337C2×C3⋊Dic3C22×D311yescharacteristic
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C4⋊(C3⋊D3)—62no—
341C4⋊(C3⋊D3)—68no—
342C4⋊(C3⋊D3)—128no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—121no—
345C4×C3⋊D3—121no—
346C4×C3⋊D3—124no—
347C4×C3⋊D3—128no—
348C3×#67—44no—
349C3×#67—68no—
350C2×C3×Dic3—34no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3C22×D314yes—
354C3×D12—28no—
355C3×D12—44no—
356C3×C4×D3—68no—
357#626—68no—
358#626—68no—
359#626—68no—
360#626—124no—
361#625—68no—
362#624—124no—
363D3×Dic3—68no—
364#534—271noSylow
365C2×C33—41no—
366C2×C33C22×D411yescharacteristic
367C2×C33H(5,𝔽2)11yescharacteristic
368C2×C33H(5,𝔽2)11yescharacteristic
369C3⋊(C3⋊D3)—22no—
370C3⋊(C3⋊D3)—41no—
371C3×C3⋊D3—22no—
372C32×D3—22no—
373C32×D3—41no—
374C32×D3—41no—
375C24×C3—34no—
376C23×D3—94no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3C2×C3⋊D311yescharacteristic, complemented
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—91no—
385C22×C3×C4—91no—
386C2×#67—34no—
387C2×#67—94no—
388C2×#67—94no—
389C2×#67—94no—
390C2×#67—94no—
391C2×#67—94no—
392C2×#67—94no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—94no—
396C2×#67—91no—
397C2×#67—184no—
398C2×#67—184no—
399C2×#67—1816no—
400C2×#67C2×C3⋊D311yescharacteristic, complemented
401C22×Dic3—94no—
402D3×D4—1816no—
403D3×D4—184no—
404C2×D12—91no—
405C2×D12—91no—
406C2×D12—91no—
407C2×D12—94no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—184no—
411C2×D12—184no—
412C2×D12C2×C3⋊D311yescharacteristic
413C2×D12C2×C3⋊D311yescharacteristic, complemented
414C2×C4×D3—34no—
415C2×C4×D3—91no—
416C2×C4×D3—94no—
417C2×C4×D3—94no—
418C2×C4×D3—91no—
419C2×C4×D3—91no—
420C2×C4×D3—184no—
421C3×C4⋊C4—91no—
422C3×C4⋊C4—91no—
423C3×C22⋊C4—24no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4D3214yescomplemented
429C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
430#217—34no—
431#217—94no—
432#217—94no—
433#217—94no—
434#217—94no—
435#217—91no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—94no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—184no—
447(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
448(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
449C4⋊Dic3—34no—
450C4⋊Dic3—94no—
451Dic3⋊C4—34no—
452Dic3⋊C4—94no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455Dic3⋊C4—184no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—32no—
464C22×C32—44no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32—61no—
474C22×C32—61no—
475C22×C32—124no—
476C22×C32C23×D314yes—
477C22×C32C23×D311yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—32no—
481C2×C3⋊D3—38no—
482C2×C3⋊D3—68no—
483C2×C3⋊D3—61no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—64no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—124no—
494C2×C3⋊D3—124no—
495C2×C3⋊D3—124no—
496C2×C3⋊D3—124no—
497C2×C3⋊D3—124no—
498C2×C3⋊D3—124no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3D3×D412yes—
501C2×C3×D3—24no—
502C2×C3×D3—24no—
503C2×C3×D3—24no—
504C2×C3×D3—24no—
505C2×C3×D3—24no—
506C2×C3×D3—24no—
507C2×C3×D3—24no—
508C2×C3×D3—24no—
509C2×C3×D3—38no—
510C2×C3×D3—416no—
511C2×C3×D3—64no—
512C2×C3×D3—64no—
513C2×C3×D3D3×D418yes—
514D32—1216no—
515D32—1216no—
516C32×C4—21no—
517C32×C4—21no—
518C32×C4—24no—
519C32×C4—24no—
520C32×C4—44no—
521C32×C4—44no—
522C32×C4—61no—
523C3⋊Dic3—21no—
524C3⋊Dic3—21no—
525C3⋊Dic3—21no—
526C3⋊Dic3—68no—
527C3⋊Dic3—61no—
528C3⋊Dic3—64no—
529C3⋊Dic3—61no—
530C3⋊Dic3—64no—
531C3⋊Dic3—124no—
532C3×Dic3—24no—
533C3×Dic3—64no—
534C3×Dic3—64no—
535C3×Dic3—64no—
536C22×D4—271no—
537C22×D4—271no—
538#123—91no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—271no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—31no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C33#53411yescharacteristic, complemented, Sylow
552C23×C3—24no—
553C23×C3—34no—
554C23×C3—34no—
555C23×C3—34no—
556C23×C3—68no—
557C23×C3—91no—
558C23×C3—124no—
559C23×C3—124no—
560C23×C3C2×D3214yes—
561C23×C3C22×C3⋊D311yescharacteristic
562C22×D3—22no—
563C22×D3—34no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—916no—
567C22×D3—94no—
568C22×D3—91no—
569C22×D3—94no—
570C22×D3—94no—
571C22×D3—91no—
572C22×D3—184no—
573C22×D3—184no—
574C22×D3—182no—
575C22×D3—188no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—364no—
581C22×D3—364no—
582C22×D3—364no—
583C22×D3—364no—
584C22×D3C22×C3⋊D311yescharacteristic
585C22×D3C22×C3⋊D311yescharacteristic
586C22×D3C22×C3⋊D311yescharacteristic
587C3×D4—68no—
588C3×D4—124no—
589C3×D4—124no—
590C3×D4—182no—
591C2×C3×C4—24no—
592C2×C3×C4—24no—
593C2×C3×C4—34no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—182no—
598C2×C3×C4C2×D3214yes—
599C2×C3×C4C2×D3214yes—
600C2×C3×C4C22×C3⋊D311yescharacteristic
601C2×C3×C4C22×C3⋊D311yescharacteristic
602#67—41no—
603#67—68no—
604#67—188no—
605#67—188no—
606#67—188no—
607#67—182no—
608#67—188no—
609#67—182no—
610#67—188no—
611#67—368no—
612#67—364no—
613#67—364no—
614#67—361no—
615#67—368no—
616C2×Dic3—34no—
617C2×Dic3—34no—
618C2×Dic3—34no—
619C2×Dic3—94no—
620C2×Dic3—94no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—184no—
624C2×Dic3—184no—
625C2×Dic3—188no—
626C2×Dic3C22×C3⋊D311yescharacteristic
627D12—22no—
628D12—41no—
629D12—182no—
630D12—188no—
631D12—182no—
632D12—182no—
633D12—182no—
634D12—368no—
635D12—361no—
636C4×D3—68no—
637C4×D3—182no—
638C4×D3—361no—
639C4×D3—364no—
640C4×D3—364no—
641C4×D3—361no—
642C4×D3—368no—
643C2×C32—24no—
644C2×C32—24no—
645C2×C32—24no—
646C2×C32—41no—
647C2×C32—44no—
648C2×C32—62no—
649C2×C32—84no—
650C2×C32—121no—
651C2×C32—121no—
652C2×C32C2×D3×D414yes—
653C2×C32C2×D3×D411yescharacteristic
654C2×C32#100414yes—
655C2×C32#100414yes—
656C2×C32#100911yescharacteristic
657C2×C32#100911yescharacteristic
658C3⋊D3—22no—
659C3⋊D3—62no—
660C3⋊D3—68no—
661C3⋊D3—128no—
662C3⋊D3—121no—
663C3⋊D3—124no—
664C3⋊D3—244no—
665C3×D3—28no—
666C3×D3—44no—
667C3×D3—44no—
668C3×D3—68no—
669C24—31no—
670C24—271no—
671C24—271no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—91no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4—544no—
686C22×C4—91no—
687C22×C4—271no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—91no—
691C4⋊C4—91no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4D3×C3⋊D311yescharacteristic, complemented
706C22×C3—24no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—24no—
713C22×C3—38no—
714C22×C3—44no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—64no—
718C22×C3—64no—
719C22×C3—64no—
720C22×C3—64no—
721C22×C3—64no—
722C22×C3—64no—
723C22×C3—64no—
724C22×C3—64no—
725C22×C3—92no—
726C22×C3—1216no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3C22×D3214yes—
730C22×C3C23×C3⋊D311yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—38no—
740C2×D3—44no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—98no—
744C2×D3—92no—
745C2×D3—188no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—364no—
762C2×D3—364no—
763C2×D3—3616no—
764C2×D3—3616no—
765C2×D3D4×C3⋊D312yes—
766C3×C4—24no—
767C3×C4—24no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—44no—
771C3×C4—44no—
772C3×C4—64no—
773C3×C4—181no—
774C3×C4—181no—
775C3×C4—181no—
776Dic3—21no—
777Dic3—64no—
778Dic3—64no—
779Dic3—64no—
780Dic3—188no—
781Dic3—184no—
782Dic3—184no—
783Dic3—181no—
784Dic3—181no—
785Dic3—364no—
786C32—24no—
787C32#558914yescomplemented
788C32#565311yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—31no—
792C23—62no—
793C23—91no—
794C23—121no—
795C23—121no—
796C23—274no—
797C23—271no—
798C23—271no—
799C23—542no—
800C23—1081no—
801C23—1081no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×C3⋊D311yescharacteristic
805D4—62no—
806D4—121no—
807D4—121no—
808D4—182no—
809D4—542no—
810D4—542no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—182no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C4—1081no—
826C2×C4—1081no—
827C2×C4C2×D3×C3⋊D311yescharacteristic
828C2×C4C2×D3×C3⋊D311yescharacteristic
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—24no—
832C2×C3—44no—
833C2×C3—41no—
834C2×C3—68no—
835C2×C3—84no—
836C2×C3—124no—
837C2×C3—124no—
838C2×C3—182no—
839C2×C3#6430714yes—
840C2×C3D32×D414yes—
841C2×C3#6431414yes—
842C2×C3C2×D4×C3⋊D311yescharacteristic
843C2×C3#6436111yescharacteristic
844C2×C3#6436111yescharacteristic
845D3—22no—
846D3—41no—
847D3—41no—
848D3—68no—
849D3—188no—
850D3—182no—
851D3—368no—
852D3—364no—
853D3—361no—
854D3—724no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—92no—
868C22—124no—
869C22—181no—
870C22—181no—
871C22—272no—
872C22—541no—
873C22—541no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22—1084no—
879C22C22×D3×C3⋊D311yescharacteristic
880C4—21no—
881C4—21no—
882C4—61no—
883C4—181no—
884C4—181no—
885C4—181no—
886C4—541no—
887C4—541no—
888C3—24no—
889C3#1059426214yescomplemented
890C3#1059606011yescharacteristic, complemented
891C2—41no—
892C2—62no—
893C2—121no—
894C2—121no—
895C2—182no—
896C2—542no—
897C2—1081no—
898C2#1172457911yescharacteristic
899C2D3×D4×C3⋊D311yescharacteristic
900C2#1172458811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D3×#638C2semidirect
2. C2×C3⋊D3×D12C2semidirect
3. #11723925C2semidirect
4. C3×#64092C2semidirect
5. C32×#882C2semidirect
6. #11723643C2semidirect
7. #11723630C2semidirect
8. #11723599C2semidirect
9. #11723540C2semidirect
10. #11723539C2semidirect
11. #11723531C2semidirect
12. #11723525C2semidirect
13. #11723518C2semidirect
14. #11723479C2semidirect
15. #11723473C2semidirect
18. C23×C32×D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C32×#67C22semidirect
29. C2×C32×D12C22semidirect
32. C2×#6291C22semidirect
33. C2×#6291C22semidirect
34. C2×#6291C22semidirect
36. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. #88857C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×C4⋊(C3⋊Dic3)C22semidirect
45. C3×#3750C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
72. #64092D3semidirect
75. C3×#882D3semidirect
101. C2×D3×C3⋊D3D4semidirect
131. C23×C3×D3C2×D3semidirect
159. C2×C4×C3⋊D3C2×D3semidirect
161. C2×C3×#67C2×D3semidirect
163. C2×C3×D12C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C2×D3semidirect
183. #3757C2×D3semidirect
189. #3752C2×D3semidirect
191. C4⋊(C3⋊Dic3)C2×D3semidirect
195. #3750C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
270. #882C3⋊D3semidirect
380. C23×D3C2×C3⋊D3semidirect
400. C2×#67C2×C3⋊D3semidirect
413. C2×D12C2×C3⋊D3semidirect
428. C3×C22⋊C4D32semidirect
429. C3×C22⋊C4C2×C3⋊D3semidirect
447. (C2×D3)⋊C4C2×C3⋊D3semidirect
448. (C2×D3)⋊C4C2×C3⋊D3semidirect
551. C33#534semidirect
705. C22⋊C4D3×C3⋊D3semidirect
787. C32#5589semidirect
788. C32#5653semidirect
889. C3#10594262semidirect
890. C3#10596060semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3×#6382
C2×C3⋊D3×D122
#117239252
C3×#640922
C32×#8822
#117236432
#117236302
#117235992
#117235402
#117235392
#117235312
#117235252
#117235182
#117234792
#117234732
#105960603
#105942623